{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian data analysis\n",
    "##  Chapter 10, demo 1\n",
    "\n",
    "Rejection sampling example\n",
    "\n",
    "In rejection sampling the proposal distribution $g(\\theta)$ has to form an envelope over the target distribution $q(\\theta)$, that is, there has to be value $M$ so that\n",
    "\\begin{equation*}\n",
    "  \\frac{q(\\theta)}{M g(\\theta)} \\leq 1.\n",
    "\\end{equation*}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# fake interesting distribution\n",
    "x = np.linspace(-3, 3, 200)\n",
    "r = np.array([ 1.1 ,  1.3 , -0.1 , -0.7 ,  0.2 , -0.4 ,  0.06, -1.7 ,\n",
    "               1.7 ,  0.3 ,  0.7 ,  1.6 , -2.06, -0.74,  0.2 ,  0.5 ])\n",
    "# Estimate the density (named q, to emphesize that it does not need to be\n",
    "# normalized). Parameter bw_method=0.48 is used to mimic the outcome of the\n",
    "# kernelp function in Matlab.\n",
    "q = stats.gaussian_kde(r, bw_method=0.48).evaluate(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rejection sampling example\n",
    "g_mean = 0\n",
    "g_std = 1.1\n",
    "g = stats.norm.pdf(x, loc=g_mean, scale=g_std)\n",
    "# M is computed by discrete approximation\n",
    "M = np.max(q/g)\n",
    "# prescale\n",
    "g *= M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFdCAYAAABPZhfMAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2ac4136a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the densities\n",
    "plt.figure(figsize=(8, 6))\n",
    "plot_tools.modify_axes.only_x(plt.gca())\n",
    "plt.plot(x, q)\n",
    "plt.plot(x, g, linestyle='--')\n",
    "plt.xlim([x[0], x[-1]])\n",
    "plt.fill_between(x, q, color=plot_tools.lighten('C0', 0.9))\n",
    "plt.legend((r'$q(\\theta|y)$', r'$Mg(\\theta)$'))\n",
    "\n",
    "# illustrate one sample\n",
    "r1 = -0.8\n",
    "zi = np.argmin(np.abs(x-r1)) # find the closest grid point\n",
    "plt.plot((x[zi], x[zi]), (0, q[zi]), color='gray')\n",
    "plt.plot((x[zi], x[zi]), (q[zi], g[zi]), color='gray', linestyle='--')\n",
    "r21 = 0.3 * g[zi]\n",
    "r22 = 0.8 * g[zi]\n",
    "plt.plot(r1, r21, marker='o', color=plot_tools.lighten('green'), markersize=12)\n",
    "plt.plot(r1, r22, marker='o', color=plot_tools.lighten('red'), markersize=12)\n",
    "# add annotations\n",
    "plt.text(x[zi], q[zi], r'$\\leftarrow \\, q(\\theta=r|y)$', fontsize=14)\n",
    "plt.text(x[zi], g[zi], r'$\\leftarrow \\, g(\\theta=r)$', fontsize=14)\n",
    "plt.text(r1-0.1, r21, 'accepted', ha='right')\n",
    "plt.text(r1-0.1, r22, 'rejected', ha='right');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get nsamp samples\n",
    "nsamp = 200\n",
    "r1 = stats.norm.rvs(size=nsamp, loc=g_mean, scale=g_std)\n",
    "zi = np.argmin(np.abs(x[:,None] - r1), axis=0)\n",
    "r2 = np.random.rand(nsamp) * g[zi]\n",
    "acc = r2 < q[zi]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAGiCAYAAACrorwAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2ac413390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the densities againg\n",
    "fig, axes = plt.subplots(\n",
    "    2, 1,\n",
    "    figsize=(8, 7),\n",
    "    sharex=True,\n",
    "    gridspec_kw=dict(\n",
    "        height_ratios=[5, 1]\n",
    "    ),\n",
    ")\n",
    "\n",
    "ax = axes[0]\n",
    "plot_tools.modify_axes.only_x(ax)\n",
    "ax.plot(x, q, label=r'$q(\\theta|y)$')\n",
    "ax.plot(x, g, linestyle='--', label=r'$Mg(\\theta)$')\n",
    "ax.fill_between(x, q, color=plot_tools.lighten('C0', 0.9))\n",
    "# the samples\n",
    "ax.scatter(\n",
    "    r1[~acc],\n",
    "    r2[~acc],\n",
    "    40,\n",
    "    color=plot_tools.lighten('red'),\n",
    "    label='rejected'\n",
    ")\n",
    "ax.scatter(\n",
    "    r1[acc],\n",
    "    r2[acc],\n",
    "    40,\n",
    "    color=plot_tools.lighten('green'),\n",
    "    label='accepted'\n",
    ")\n",
    "ax.legend()\n",
    "\n",
    "# only accepted samples \n",
    "ax = axes[1]\n",
    "ax.scatter(r1[acc], np.ones(np.count_nonzero(acc)), 40, color='#4daf4a', alpha=0.3)\n",
    "ax.set_yticks(())\n",
    "ax.set_xlim((x[0], x[-1]))\n",
    "\n",
    "# add inter-axis lines\n",
    "transf = fig.transFigure.inverted()\n",
    "for i in range(nsamp):\n",
    "    if acc[i] and x[0] < r1[i] and r1[i] < x[-1]:\n",
    "        coord1 = transf.transform(axes[0].transData.transform([r1[i], r2[i]]))\n",
    "        coord2 = transf.transform(axes[1].transData.transform([r1[i], 1]))\n",
    "        fig.lines.append(mpl.lines.Line2D(\n",
    "            (coord1[0], coord2[0]),\n",
    "            (coord1[1], coord2[1]),\n",
    "            transform=fig.transFigure,\n",
    "            alpha=0.2\n",
    "        ));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAdkAAAFqCAYAAABWGSDZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nmvw/W7fI/TTOTwcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff2aa1e0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# alternative proposal distribution\n",
    "g = np.empty(x.shape)\n",
    "g[x <= -1.5] = np.linspace(q[0], np.max(q[x<=-1.5]), len(x[x<=-1.5]))\n",
    "g[(x > -1.5) & (x <= 0.2)] = np.linspace(\n",
    "    np.max(q[x<=-1.5]),\n",
    "    np.max(q[(x>-1.5) & (x<=0.2)]),\n",
    "    len(x[(x>-1.5) & (x<=0.2)])\n",
    ")\n",
    "g[(x > 0.2) & (x <= 2.3)] = np.linspace(\n",
    "    np.max(q[(x>-1.5) & (x<=0.2)]),\n",
    "    np.max(q[x>2.3]),\n",
    "    len(x[(x>0.2) & (x<=2.3)])\n",
    ")\n",
    "g[x > 2.3] = np.linspace(np.max(q[x>2.3]), q[-1], len(x[x>2.3]))\n",
    "M = np.max(q/g)\n",
    "g *= M\n",
    "\n",
    "# plot\n",
    "plt.figure(figsize=(8, 6))\n",
    "plot_tools.modify_axes.only_x(plt.gca())\n",
    "plt.plot(x, q)\n",
    "plt.plot(x, g, linestyle='--')\n",
    "plt.fill_between(x, q, color=plot_tools.lighten('C0', 0.9))\n",
    "plt.legend((r'$q(\\theta|y)$', r'$Mg(\\theta)$'))\n",
    "plt.xlim([x[0], x[-1]])\n",
    "plt.title('alternative proposal distribution');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
